Table 3 Parameters of marginal distribution functions of flood variables

Gamma

\(\frac{1}{{b^{a} \Gamma (a)}}x^{a - 1} e^{{ - \frac{x}{b}}}\), \(\Gamma (a) = \int_{0}^{\infty } {u^{a - 1} e^{ - u} du}\)

a

b

GEV

\((\frac{1}{\sigma })\exp ( - (1 + k\frac{(x - \mu )}{\sigma })^{{ - \frac{1}{k}}} )(1 + k\frac{(x - \mu )}{\sigma })^{{ - 1 - \frac{1}{k}}}\)

k

μ

σ

Lognormal

\(\frac{1}{{x\sqrt {2\pi \sigma_{y} } }}\exp ( - \frac{{(y - \mu_{y} )}}{{2\sigma_{y}^{2} }})\)

y = log(x), x > 0, – ∞ < μ_y < ∞, σ_y > 0

μ_y

σ_y